Refer to the attached files.

1.2(c). Some of the optimization problems in this part (Part 1.2) are formally (mathematically) identical to some of the ones in Part 1.1 above. Which ones are those? Explain. 1.2(d). Interpret the Lagrange multipliers A(p, w) and u(p,u). 1.1(e). Show that if u* = v(p,w*), then A(p,w#) =- 1 "(p.*) Interpret. (Hint. Use duality.) 1.2(f). Let * =q(p,r) and u* = (x*). Show that r= u(p,w*) and interpret. 1.1(g). Let * = q(p,r), * = (x*)and w*=e(p,w*). Show that r= and A(p,w# ) interpret.